Tetra Slice

Why use this problem?

This problem uses vectors to describe the edges of shapes, and to prove the properties of shapes.  

For the extension, pupils might like to use the scalar product to find some lengths (or use a geometrical argument as we know facts about the lengths and angles in a regular tetrahedron).

Key Questions

• If the position vector of $A$ is $\overrightarrow{OA} = {\bf a}$, how could we describe $\overrightarrow{AB}$?
• Can you express $\overrightarrow{PQ}$ in terms of some or all of ${\bf a}, {\bf b}, {\bf c}, {\bf d}$?
• If ${\bf a} = k{\bf b}$, what does that tell us about the vectors ${\bf a}$ and ${\bf b}$?